If I open a bottle of Belgian beer-with a cork- drink a little then put the cork back in the bottle will the cork randomly pop or the bottle explode from any pressure?
Yes, you can do this just like a bottle of sparkling wine. It should keep the beer for a couple of days, but not forever. Sometimes the corks don't work great, so I would buy a Champagne bottle stopper like the one below Don't get the one that hold onto the ridge under the bottle opening. They work great for Champagne bottles but not so good on Belgian beer bottles.
After opening the bottle the beer will begin to oxidize and degrade in quality, so flavor will begin to suffer shortly after opening.
Pressure will not continue to build in the bottle from fermentation, the yeast have consumed what residual sugar is present for bottle carbonation. That being said, the dissolved CO2 will remain in solution at cooler temperatures but escape rapidly as it warms, so capping while the bottle is cool and keeping the bottle cool will preserve more CO2 in solution after opening.
A recorked bottle will be most likely to drive out the cork if allowed to warm, or agitated physically.
A recorked bottle will be less likely to drive out the cork, if recorked warm, and then placed gently into cold storage.
Lastly, volumes of CO2 in Belgian beers can range wildly, but their level of CO2 is generally higher than domestic US beer, however much lower than champagne. Pressure in the bottle will react as such.